On the resistance regular graphs

For a connected graph $G$, its resistance matrix is denoted by $R(G)$. If all the row(column) sums of $R(G)$ are equal, then $G$ is said to be resistance regular. We provide some necessary and sufficient conditions for a simple connected graph to be a resistance regular graph. Also, we determine various bounds for the resistance energy and resistance spectral radius of $G.$ Furthermore, we compute the resistance spectrum and resistance energies of some resistance regular graphs.